We introduce a methodical approach for
deriving governing equations for porous materials called
Hybrid Mixture Theory. Hybrid Mixture Theory
is a combination of volume averaging the field equations
(conservation of mass, momentum, energy) and exploiting
the entropy generation inequality to obtain constitutive
equations (additional, material-dependent equations needed
to close the system). We will demonstrate the
Coleman and Noll method of exploiting the entropy
generation inequality to derive the Navier-Stokes
equation, discuss the averaging procedure, and provide
results regarding macroscopic flow for swelling porous
materials such as drug-delivery polymers, expansive soils,
soybeans, and biotissues. In particular we
will (briefly) discuss existence, uniqueness, and a
numerical approach for solving a nonlinear Volterra
partial integro-differential equation.
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